108 citations · 148 across the 7 of their papers we have counts for
7 papers
Elliptic Quantum Toroidal Algebra and Elliptic Stable Envelopes for the Quiver Varieties
Hitoshi Konno, Andrey Smirnov
We propose a new construction of vertex operators of the elliptic quantum toroidal algebra by combining representations of the algebra and fo…
Quantum Difference Equations for Grassmannians
Xingyu Cheng, Reese Lance, Nikhil Nagabandi +1
We consider quantum difference equation (QDE) for equivariant quantum K-theory of the Grassmannian. In this paper we obtain a solution to the QDE and use the solution to asymptotic…
Enumerative geometry via elliptic stable envelope
Andrey Smirnov
Assume is a variety for which the elliptic stable envelope exists. In this note we construct natural -difference equations from the elliptic stable envelope of . In examp…
Elliptic Quantum Toroidal Algebra U_{t_1,t_2,p}(gl_{1,tor}), Vertex Operators and L-operators
Hitoshi Konno, Andrey Smirnov
We propose new vertex operators, both the type I and the type II dual, of the elliptic quantum toroidal algebra U_{t_1,t_2,p}(gl_{1,tor}) by combining representations of U_{t_1,t_2…
On genus expansion of superpolynomials
A. Mironov, A. Morozov, A. Sleptsov +1
Recently it was shown that the (Ooguri-Vafa) generating function of HOMFLY polynomials is the Hurwitz partition function, i.e. that the dependence of the HOMFLY polynomials on repr…
Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)
Petr Dunin-Barkowski, Alexey Sleptsov, Andrey Smirnov
We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $…
Superpolynomials for toric knots from evolution induced by cut-and-join operators
P. Dunin-Barkowski, A. Mironov, A. Morozov +2
The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R…